3-TRIANGULATIONS OF POLYHEDRA AND THEIR CONNECTION GRAPHS

Milica Stojanović

DOI Number
https://doi.org/10.22190/FUMI240723051S
First page
771
Last page
784

Abstract


Here we investigate the properties of 3-triangulation of polyhedra, when
possible. Namely, it is known that 3-triangulation of convex polyhedra is always possible, but this is not the case with all non-convex ones. This is the reason to consider the decomposition of non-convex polyhedra into convex pieces if possible. After that, we introduce the connection graph for the 3-triangulable polyhedron in such a way that these pieces are represented by the nodes of the graph. First, our attention shall be focused on toroids, a special class of non-convex polyhedra, and the minimal number of tetrahedra necessary to 3-triangulate them. As another application of connection graphs, we shall also consider those corresponding to convex polyhedra, especially to conic triangulation of them.


Keywords

3-triangulation, conic triangulation, non-convex polyhedra.

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References


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DOI: https://doi.org/10.22190/FUMI240723051S

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